The koi, or ornamental carp, is a very popular symbol in Japanese tattooing and it's popularity has carried over with Western fans of Japanese-style ink. Like many other elements of Japanese culture, koi have their roots in Chinese culture and were absorbed into the history and myths of Japan many thousand years ago.
The ancestors of these colorful fish were mostly plain brown in color, and were kept in rice paddies to help eat insects and to supplements the farmer's diet. At some point, the occasional carp that wasn't brown or which displayed markings started to be kept and bred for appearances and variations. Starting in the last 17th and early 18th centuries, this selective breeding began producing a fanciful array of colors and some distinctive marking patterns and the attraction of koi spread to Japan. After a major international exhibition of koi in the early 20th century, the tradition of keeping and breeding koi grew in popularity, leading to the fish which are popular with collectors around the world today.
The mythology and symbolism of koi connotes courage, strength and perseverance, especially in the face of adversity. The ancient stories say that only the most determined koi can swim upstream, and if they can leap the waterfalls and go upstream, they will be rewarded by being turned into dragons. These fish are often a considered a sign of good luck, especially the golden carp.
Their variety of colors and markings make them an adaptable tattoo design, fitting in with a variety of styles, whether realistic or fantastical. They can be drawn on a small scale for an arm or leg, or enlarged to stand alone as a bold back piece. Their curving or straight body lines allowed them to be fitted into a variety of spaces and shapes on the human figure. They are often depicted amidst watery waves, along with chrysanthemums which are also considered symbolic of strength and dignity.
If you'd like to read more on Japanese tattoos, you can see more of Japanese koi tattoos, or check out more about the Japanese style of tattoos in general.